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The Product of Automorphic Weighted Composition Operators on Hardy Space H <sup>2</sup>
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Abstract<p>Let <inline-formula> <tex-math><?CDATA $n\in {\mathbb{N}},{p}_{i}\in {\rm{U}},{\alpha }_{{P}_{i}}(z)=\frac{{p}_{i}-z}{1-{\bar{p}}_{i}z}(z\in {\rm{U}})$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>n</mi> <mo>∈</mo> <mi>ℕ</mi> <mo>,</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>z</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mi>i</mi> </msub> <mi>z</mi> </mrow> </mfrac> <mo stretchy="false">(</mo> <mi>z</mi> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo stretchy="false">)</mo> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula>, and let <inline-formula> <tex-math><?CDATA ${f}_{1}\in {H}^{\infty },i=1,\ldots,n$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>∈</mo> <msup> <mi>H</mi> <mi>∞</mi> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>. We discuss the relation between the points <italic>p<sub>i</sub> </italic> in U and the functions <italic>f<sub>i</sub> </italic> in U and the properties of the product of automorphic weighted composition operators <inline-formula> <tex-math><?CDATA ${W}_{{f}_{1},{\alpha }_{{p}_{1}}}\,{W}_{{f}_{2},{\alpha }_{{p}_{2}}}\ldots {W}_{{f}_{i},{\alpha }_{pi}}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </msub> <mspace width="0.25em"></mspace> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>…</mo> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> on Hardy space H<sup>2</sup>. In fact, it is very nice connection between analytic function theory and operator theory. In this paper, we give the sufficient and necessary conditions to be normal, unitary, hermitian operator on <italic>H</italic> <sup>2</sup> and we shall present the shape of the numerical range of it.</p>
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Publication Date
Mon Jan 02 2017
Journal Name
Al-academy
Style and the jump in industrial product design - a comparative study
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Find cares studying ways in the development of industrial products and designs: the way the progressive development (how typical) and root development (jump design), was the aim of the research: to determine the effectiveness of the pattern and the jump in the development of designs and industrial products. After a process of analysis of a sample of research and two models of contemporary household electrical appliances, it was reached a set of findings and conclusions including:1-leaping designs changed a lot of entrenched perceptions of the user on how the product works and its use and the size and shape of the product, revealing him about the possibilities of sophisticated relationships with the product, while keeping the typical desi

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Publication Date
Sat Oct 28 2023
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Diversity Operators-based Artificial Fish Swarm Algorithm to Solve Flexible Job Shop Scheduling Problem
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Artificial fish swarm algorithm (AFSA) is one of the critical swarm intelligent algorithms. In this
paper, the authors decide to enhance AFSA via diversity operators (AFSA-DO). The diversity operators will
be producing more diverse solutions for AFSA to obtain reasonable resolutions. AFSA-DO has been used to
solve flexible job shop scheduling problems (FJSSP). However, the FJSSP is a significant problem in the
domain of optimization and operation research. Several research papers dealt with methods of solving this
issue, including forms of intelligence of the swarms. In this paper, a set of FJSSP target samples are tested
employing the improved algorithm to confirm its effectiveness and evaluate its ex

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Publication Date
Mon Mar 25 2019
Journal Name
Al-academy
The Effectiveness of Implication in New Formulations of the Contemporary Industrial Product: زياد حاتم حربي
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  The current research aims at transforming the concept of implication from the rhetoric into the industrial design in order to have a new term (the design implication) in which the industrial designer takes all or part of another's design to imply his design in it and acknowledge that, and if he did not do so, it would be (design theft) parallel to the literary plagiarism.
In order to show the potentials of the industrial design in the production of new formulations of the industrial products forms, as the design is the carrier of language that addresses the recipients, it is possible to use the implication as a the tool of literature in the design and as a design strategy as it is one of the concepts that takes its course in e

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Publication Date
Sun Jun 01 2008
Journal Name
Baghdad Science Journal
Studying of the complexes product of the nerve agent Soman with the Butyrylcholinesterase and Acetylcholinesterase Enzymes
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Cholinesterases are among the most efficient enzymes known. They are divided into two groups: acetylcholinesterase (AChE) involved in the hydrolysis of the neurotransimitter acetylcholine, and butyrylcholinesterase (BChE) of unknown function. Several crystal structures of the former have shown that the active site is located at the bottom of a deep and narrow gorge. Human BChE has attracted attention because it can hydrolyze toxic esters and nerve agents. Here we analyze the complexes of cholinesterase with soman by describing the 3D geometry of the complex, the active site, the changes happened through the inhibition and provide a description for the mechanism of inhibition. Soman undergoes degradation in the active site of the AChE and B

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Publication Date
Sun Mar 09 2008
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Um-salama Science Journal
Studying of the complexes product of the nerve agent Soman with the Butyrylcholinesterase and Acetylcholinesterase Enzymes
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Cholinesterases are among the most efficient enzymes known. They are divided into two groups: acetylcholinesterase (AChE) involved in the hydrolysis of the neurotransimitter acetylcholine, and butyrylcholinesterase (BChE) of unknown function. Several crystal structures of the former have shown that the active site is located at the bottom of a deep and narrow gorge. Human BChE has attracted attention because it can hydrolyze toxic esters and nerve agents. Here we analyze the complexes of cholinesterase with soman by describing the 3D geometry of the complex, the active site, the changes happened through the inhibition and provide a description for the mechanism of inhibition. Soman undergoes degradation in the active site of the AChE and BC

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Publication Date
Tue Dec 01 2020
Journal Name
Baghdad Science Journal
The Numerical Technique Based on Shifted Jacobi-Gauss-Lobatto Polynomials for Solving Two Dimensional Multi-Space Fractional Bioheat Equations
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This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

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Publication Date
Tue Dec 01 2015
Journal Name
The Journal Of The Acoustical Society Of America
Underdetermined reverberant acoustic source separation using weighted full-rank nonnegative tensor models
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In this paper, a fusion of K models of full-rank weighted nonnegative tensor factor two-dimensional deconvolution (K-wNTF2D) is proposed to separate the acoustic sources that have been mixed in an underdetermined reverberant environment. The model is adapted in an unsupervised manner under the hybrid framework of the generalized expectation maximization and multiplicative update algorithms. The derivation of the algorithm and the development of proposed full-rank K-wNTF2D will be shown. The algorithm also encodes a set of variable sparsity parameters derived from Gibbs distribution into the K-wNTF2D model. This optimizes each sub-model in K-wNTF2D with the required sparsity to model the time-varying variances of the sources in the s

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Publication Date
Wed Mar 15 2023
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Kinetic diversity and its effectiveness in the formal variables of industrial product design
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The formal diversity in designs is achieved by creating shapes and lines with a distinct movement pattern, which are preceded by mental processes. The greatest source of diversity in design in general and industrial design in particular is the creation of multiple directions for the completion of designs and the diversification of intellectual proposals for the design idea. The human activity that takes place around us in various fields of life takes place due to the diversity of movement in the form of the design product and its effectiveness through the dynamic diversity in the form, which differs in the methods of designing and showing it. He invents material value as a distinct artistic product that he owns A specific form or system

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Publication Date
Mon Dec 20 2021
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
IMPACT OF THARTHAR ARM WATER ON COMPOSITION AND DIVERSITY OF COPEPODA IN TIGRIS RIVER, NORTH OF BAGHDAD CITY, IRAQ
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This study is considered to be the first on this sector of Tigris River after 2003, to evaluate the effect of Tharthar Arm on the composition and diversity of Copepoda in Tigris River. Six sampling sites were selected; two on the Tharthar Arm and four sites along the Tigris River, one before the confluence as a control site and the others downstream the confluence; thirty-five copepod taxa were recorded, 34 taxa in the Tigris River and 25 taxa in the Tharthar Arm.
The highest density of Copepoda was in site 2 at Tharthar Arm was 265584.2 Ind./m3 lead to an increasing in Copepoda density in Tigris River from 63878.2 Ind./m3 in site 1 before the confluence to 127198.3 Ind./m3 in site 4 immediately downstream the confluence. Also, the me

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Publication Date
Tue Mar 01 2016
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Al-academy
Metaphor in product design: قيس والي عباس
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Addresses current research to the subject of metaphor as a field important in the design of industrial product, so it was a problem search: Does industrial product which is designed mainly to reflect the principle of metaphor role in receiving, and how the application of mechanisms theory correct as stipulated in institutions metaphor properly for this orientation in achieving those metaphors. What are the relations of reciprocity that influenced the establishment of the design and construction of the system for industrial product, the objectives of the research were standing on the interactive nature of the relations between the metaphor and the process of industrial product design? And identify strengths and weaknesses in the processes

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